Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Page concordance

< >
Scan Original
231 498
232 499
233 500
234 501
235 502
236 503
237 504
238 505
239 506
240
241
242
243 507
244 508
245 509
246 510
247 511
248 512
249 513
250 514
251 515
252 516
253 517
254 518
255 519
256 520
257
258
259
260
< >
page |< < (486) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div240" type="section" level="1" n="119">
          <p>
            <s xml:id="echoid-s4523" xml:space="preserve">
              <pb o="486" file="0206" n="216" rhead="CHRIST. HUGENII"/>
            rallela A B. </s>
            <s xml:id="echoid-s4524" xml:space="preserve">Si verò non habeatur omnino l, recta I K in
              <lb/>
            A B incidere intelligenda eſt.</s>
            <s xml:id="echoid-s4525" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4526" xml:space="preserve">Deinde ſicut z ad n, quæ ratio data, ita ſit I K ad libi-
              <lb/>
            tum ſumpta, ad K L; </s>
            <s xml:id="echoid-s4527" xml:space="preserve">quæ ipſi A I parallela ducendaeſt, ſu-
              <lb/>
            mendaque hoc pacto, ut puncta K L ſita ſint quo ordinc
              <lb/>
            A I, ſi habeatur + {nx/z}, at contrà ſi habeatur - {nx/z}, & </s>
            <s xml:id="echoid-s4528" xml:space="preserve">du-
              <lb/>
            catur recta per IL; </s>
            <s xml:id="echoid-s4529" xml:space="preserve">ſi verò deſit {nx/z}, eadem eſt I L & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">I K.</s>
            <s xml:id="echoid-s4531" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4532" xml:space="preserve">Porro ut p ad g, ita ſit {1/2}o ad ſingulas IX, I Y ſumendas
              <lb/>
            in recta A I; </s>
            <s xml:id="echoid-s4533" xml:space="preserve">atque ita quoque I X ad I V ſumendam in I K
              <lb/>
            ad partes A B ſi habeatur - o x, aut in contrarias ſi habea-
              <lb/>
            tur + ox; </s>
            <s xml:id="echoid-s4534" xml:space="preserve">& </s>
            <s xml:id="echoid-s4535" xml:space="preserve">ſit V M parallela A I, occurratque rectæ I L
              <lb/>
            in M: </s>
            <s xml:id="echoid-s4536" xml:space="preserve">erit jam M centrum hyperbolæ quæſitæ aſymptoti
              <lb/>
            vero, rectæ per M X, M Y ductæ.</s>
            <s xml:id="echoid-s4537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4538" xml:space="preserve">Si vero non habeatur o x in æquatione, erit I centrum hy-
              <lb/>
            perbolæ; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">ſumptisque I X, I Y ad libitum ſed inter ſe æqua-
              <lb/>
            libus, inventiſque inde punctis V & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">M, ut ante, ducentur
              <lb/>
            aſymptoti per I parallelæ ipſis M X, M Y.</s>
            <s xml:id="echoid-s4541" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4542" xml:space="preserve">Jam porro ſi habeatur + mm, puncta S & </s>
            <s xml:id="echoid-s4543" xml:space="preserve">R, per quæ
              <lb/>
            hyperbola vel oppoſitæ ſectiones tranſire debent, invenien-
              <lb/>
            tur ſumendo in recta A I à puncto I, ſingulas I S, I R æqua-
              <lb/>
            les m: </s>
            <s xml:id="echoid-s4544" xml:space="preserve">unde jam hyperbola data erit ac deſcribi poterit, in
              <lb/>
            qua B C erit ordinatim applicata ad diametrum, ſi {{1/2}og/z} ma-
              <lb/>
            jor quam m; </s>
            <s xml:id="echoid-s4545" xml:space="preserve">ſin verò {{1/2}og/p} minor quam m, erit B C paralle-
              <lb/>
            la diametro hyperbolæ ad quam eſt C punctum, ut hic caſu
              <lb/>
            ſecundo. </s>
            <s xml:id="echoid-s4546" xml:space="preserve">Quod ſi forte punctum S incidat in X, locus
              <lb/>
            puncti C, erunt ipſæ aſymptoti. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">Si verò non habeatur mm,
              <lb/>
            erit ipſum I punctum in hyperbola quæſita.</s>
            <s xml:id="echoid-s4548" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4549" xml:space="preserve">At ſi habeatur — mm, accommodanda eſt intra angu-
              <lb/>
            lum X M I recta G N parallela I X, quæque poſſit quadrata
              <lb/>
            @b I X & </s>
            <s xml:id="echoid-s4550" xml:space="preserve">I S, vel tantum ipſi I S æqualis, ſi non </s>
          </p>
        </div>
      </text>
    </echo>
Impressum